Teaching Foundation Mathematics

A Guide for Teachers of Older Students with Learning Difficulties

Nadia Naggar-Smith

• Publisher: Routledge
• Year: 2008
• Print ISBN: 9781138401228
• eBook ISBN: 9781134057368
• Edition: 1
• Topic: Education
• Subtopic: Education General

This fully photocopiable resource will provide essential materials for anyone teaching pre-entry or foundation Maths in secondary schools and further education. Teaching Foundation Mathematics is developed to provide age appropriate material for adult learners with moderate to severe learning difficulties and/or disabilities and for children, over twelve, with special needs. It will also prove useful to teachers training to work with these learners.

Thirty ready-to-use lessons are at your fingertips in this book, complete with tutor's notes, teaching objectives, detailed lesson plans and photocopiable worksheets, where appropriate. The lessons are divided into three areas – number, shape and measure.

Part I
Number

Introduction to Number

Numeracy

When the word ‘numeracy’ was first introduced in the Crowther Report in 1959, it related to a sophisticated level of mathematical understanding to be found in the sixth form curriculum and to the application of mathematics. Later, it was widely used to describe the ability to perform basic arithmetic operations. This later definition was responsible for the restricted curriculum offered to students with learning difficulties.

It was not until the publication of the Cockcroft Report, in 1982, that it was given its current meaning. This report recommended that the word ‘numerate’ should imply the possession of two attributes:

1. an ability to make use of mathematical skills, which enables an individual to cope with the practical mathematical demands of his or her everyday life;
2. an ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance charts, tables and graphs.

In that report the basic skills for adult life are given as an ability:

• to read numbers and to count;
• to tell the time;
• to pay for purchases and to give change;
• to weigh and to measure;
• to estimate and approximate;
• to understand straightforward timetables and simple graphs and charts; and
• to carry out any necessary calculations associated with these.

Most important of all is the need to have sufficient confidence to make effective use of whatever mathematical skill and understanding is possessed, whether this be little or much.

The recommendations of the Cockcroft Report form the foundations of both the mainstream National Curriculum for Mathematics and the National Numeracy Strategy for England.

Number

The Adult Pre-entry Curriculum Framework for Numeracy aims to make students numerate to a level commensurate with their ability. The teaching and learning elements are: Number, Measure, Shape and Space, and Handling Data.

In preparation for the Adult Numeracy core curriculum, students will work towards mastery of the following skills:

• counting to ten;
• comparing quantities to five;
• reading, writing and ordering numerals to ten;
• counting sets of objects to ten;
• adding to ten;
• subtracting to ten;
• using ordinal numbers from first to fifth;
• understanding and applying the addition, minus and equal symbols; and
• understanding simple bar charts.

The Number lessons in this book have been carefully planned to provide students with an opportunity to build a Number Tool Kit for use in everyday life and to take with them when they progress to the core curriculum.

The Number section of this book offers suggestions for ten lessons to assist in the teaching and learning of number. Each lesson is directly linked to the Adult Pre-entry Curriculum Framework for Numeracy and the P scales.

References

Crowther Report 15 to 18 (1959): A report of the Central Advisory Council for Education England, HMSO London.

Mathematics Counts (1982): Report of the Committee of Inquiry into the Teaching of Mathematics in Schools under the Chairmanship of Dr W.H. Cockcroft, HMSO London.

Lesson N1—Cardinal numbers

Tutor’s notes

This lesson helps to develop concepts of cardinality up to five, through visualisation of quantities. Most adults, but not all, can see quantities to about six, without having to count them (subitising). Although your students should be comfortable with visual quantities up to five, you may need to adjust the number to four. Sometimes you may encounter a student with a specific learning difficulty who cannot subitise; this lesson may not be suitable for such students, but try building the activity gradually with numbers one, then two, to as far as they can go.

When preparing visual number cards, it is important not to group the spots or objects in familiar pattern forms, for example those used on dice or playing cards, as there is a possibility of students relating the quantity only to the number pattern. Patterns become important after the concept has been developed.

When using visual number cards, they remain on the overhead projector (OHP) to the silent count of three and are then withdrawn, as the presenter says, ‘Say it fast’. This prompts students to visually remember what they saw.

An alternative way of using the cards is to have two students working together at the OHP. One student puts the cards down and the other takes them off. The remaining students watch the screen and say how many spots they can see, as fast as they can.

The lesson lays the foundations for mental mathematics and progresses to requiring students to hold the visual number of spots in their ‘mind’s eye’, while adding or subtracting one. Nothing is recorded during this activity.

The worksheets encourage students to discuss, remember and record what they did during the activity. This forms a link between this visualisation and the beginning of recorded mathematics. This same systematic approach used in the mental addition activity can be used for mental subtraction. A recording sheet is included for this.

Criteria

Adult Pre-entry Curriculum Framework for Numeracy

Number

Milestone 6—sub-element 3

Milestone 7—sub-element 2 and sub-element 4

Milestone 8—sub-element 3 and sub-element 6

P scales

Using and applying mathematics P8

Number P8

Lesson N1 Cardinal numbers

Objectives

• to recognise quantities without counting;
• to strengthen visual memory;
• to create foundations for addition and subtraction.

Resources

• A5 cards with holes punched in them:
  One set of cards comprises 5 cards with 1, 2, 3, 4 or 5 holes in them. Make a further set with the holes positioned differently.
  
  Alternatively, prepare squares of OHP transparencies with coloured spots on them.
• Worksheet 1—one copy for each student;
• Worksheet 2—one copy for each student;
• OHP and screen.

Lesson plan

Stage 1: Introduction and class discussion

1. Shuffle the spot ...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Introduction
• PART I Number
• PART II Measure
• PART III Shape